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In this topic, we will learn the definition of a numerical expression, what is the meaning of numerical and learn how to write a number in numerical form. We will discuss here the simplification of numerical expressions. Students will be provided with plenty of examples to clearly illustrate this important mathematical concept. When we look at a problem with numbers, we are most likely looking at a numerical expression. In this article, we will explain how to simplify numerical expressions with the help of various numerical expression examples.

Numerical Definition-The term numerical means involving numbers.

The term numerical expression consists of two words, numerical meaning numbers, and expression meaning phrase. Thus, it is a phrase involving numbers. A numerical expression in mathematics is a combination of numbers, integers combined using mathematical operators such as addition, subtraction, multiplication, or division.

There are different forms in which the number can be expressed such as word form and numerical form.

A numerical expression is a mathematical statement that involves only numbers along with one or more operation symbols. Examples of operation symbols are addition, subtraction, multiplication and division. It can also be expressed in the radical symbol (the square root symbol) or the absolute value symbol.

A numerical expression is formed by the combination of numbers including various mathematical operators. There is no limit to the number of operators that a numerical expression may contain. Some numerical expressions use only one operator between two numbers whereas some may contain more than one.

The only requirements for a numerical expression are that it only contains numbers and operation symbols. Some numerical expressions have only one operation symbol. Others have two or more.

Here are Some Examples of Numerical Expressions:

4 + 5

134 - 75

56 * 4 + 6

\[\frac{60}{5}\] * 7 - 2 + 1

As we know numerical expressions can only contain numbers, expressions containing variables (such as x or y) cannot be considered numerical expressions. They are actually called algebraic expressions instead. Given below are two examples of algebraic expressions:

2x + 5

250 - y

Any mathematical word problem is solved by first converting it into a numerical expression.

Below we have provided one example to understand it.

Question: Nancy has 10 chocolate bars. She gives 3 chocolates to her sister, 1 to her friend and eats 2. Later she visits her grandmother, and she (grandmother) offers Nancy 12 more chocolate bars. How many chocolate bars does Nancy have now?

Solution: Here first look at the numbers involved in the above problem. Nancy has 10 chocolate bars. She gives away 4 (3 to her sister and 1 to her friend), eats 2 and then again gets 12 chocolate more from her grandmother. So, it can be represented in numerical expression as 10 - 3 - 1 - 2 + 12

= 7 - 1 - 2 + 12

= 6 - 2 + 12

= 4 + 12

= 16

Hence, Nancy has now 16 chocolate bars.

Power can also be expressed as a numerical expression. It has two parts: an exponent and a base.

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2⁴ can be written as 2.2.2.2

An expression can also be a combination of variables and constants, that are combined using mathematical operations. Such expression is known as an algebraic expression.

To simplify a numerical expression that has two or more operations, we perform the BODMAS rule. In this rule we have to solve operations like Division first, followed by Multiplication, Addition and then Subtraction. A standard result called BODMAS is followed for simplification of these operations.

The word BODMAS stands for:

B → Brackets

O → of means (Multiplication ×)

D → Division

M → Multiplication

A → Addition

S → Subtraction

If the brackets are present in the problem, first we have to simplify the brackets. There are four kinds of brackets.

( ) → This symbol is simple brackets or round brackets or parenthesis.

{ } → Braces or Curly brackets.

[ ] → Square brackets.

______ → This symbol is a line called bar or vinculum. It is used when two or more types of brackets are involved in the problem. Brackets are removed in this order ‘_________’, ( ), { }, [ ].

(i) Solve [10 + {7 - (8 ÷ 2)}] × 3

First, we will solve the round bracket

= [10 + {7 - 4}] × 3

Now remove the curly bracket

= [10 + 3] × 3

Finally,remove the square bracket

= 13 × 3

= 39

Hence the final value is 39

(ii) Find the Value of : 15 + [20 - {8 + (6 ÷ 2)}]

First, remove the round bracket

= 15 + [20 - {8 + 3}]

Now, remove the curly bracket

= 15 + [20 - 11]

Lastly, remove square brackets

= 15 + 9

= 24

Hence the final value is 24

(iii) Evaluate the Numerical Expression 10² - 10 + 100

Fist evaluate the square value

= 10 x 10 - 10 + 100

=100-10+100

=90+100

=190

Hence the final value is 190.

FAQ (Frequently Asked Questions)

1. What is a Numerical Expression?

Ans: A numerical expression is a mathematical expression involving only numbers and one or more operational symbols.

2. How are Real-world Problems in Which We Use the Numerical Expression?

Ans: There are numerous real-life situations that we can solve easily with the help of numerical expressions. Various examples are when we need to find how much discount is applied to a product, to find the area of a rectangular park, to find the number of ingredients required to make pizza and so on.

3. What are the Steps Needed to Follow While Solving Numerical Expression?

Ans: Following are the steps to solve numerical expression:

**Step 1: **First simplify the operations inside grouping symbols.

**Step 2: **Simplify the powers.

**Step 3: **Solve multiplication and division followed by a left to right.

**Step 4:** Finally solve addition and subtraction from left to right.